The main goal of this section is to use \(\star \) -trisections to draw diagrams for closed 4-manifolds obtained by various kinds of surgery.
Drawings for these 4-manifolds could be theoretically derived using previous work on relative trisections. However, the genus of these diagrams will often be large.
For example, in [1]}, a genus seven trisection of \(T^2\times S^2\)  was obtained by taking the double of a genus 3 relative trisection for \(T^2\times D^2\) .
In Figure REF , we used a genus one \(\star \) -trisection for \(T^2\times D^2\)  to draw a genus four trisection for \(T^2\times S^2\) .
This section provides diagrams for the Cacime Surface (Section REF ), and algorithms to perform Fintushel-Stern knot surgery (Section REF ) and torus surgeries (Section REF ) such as Logarithmic transforms and Luttinger transforms.
The careful reader might observe that the diagrams for these transformations change by concatenating a fixed picture or by changing some loops in a high enough stabilization of the original trisection diagram. Thus to study the behavior of 4-manifold invariants under surface surgery, it could be worthwhile to explore each local modifications in detail.
